Background-independent measurement of θ[subscript 13] in Double Chooz

(1)

Background-independent measurement

of #[subscript 13] in Double Chooz

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Citation

Abe, Y., et al. “Background-independent measurement of

θ[subscript 13] in Double Chooz.” Physics Letters B 735 (July 2014):

51–56.

As Published

http://dx.doi.org/10.1016/j.physletb.2014.04.045

Publisher

Elsevier

Version

Final published version

Citable link

http://hdl.handle.net/1721.1/98040

Terms of Use

Creative Commons Attribution

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Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Background-independent measurement of

θ

₁₃

in Double Chooz

Double Chooz Collaboration

Y. Abe

ab

, J.C. dos Anjos

e

, J.C. Barriere

n

, E. Baussan

v

, I. Bekman

a

, M. Bergevin

i

,

T.J.C. Bezerra

z

, L. Bezrukov

m

, E. Blucher

f

, C. Buck

s

, J. Busenitz

b

, A. Cabrera

d

, E. Caden

j

,

L. Camilleri

h

, R. Carr

h

, M. Cerrada

g

, P.-J. Chang

o

, E. Chauveau

z

, P. Chimenti

ae

,

A.P. Collin

n

, E. Conover

f

, J.M. Conrad

r

, J.I. Crespo-Anadón

g

, K. Crum

f

, A. Cucoanes

w

,

E. Damon

j

, J.V. Dawson

d

,

ah

, D. Dietrich

ad

, Z. Djurcic

c

, M. Dracos

v

, M. Elnimr

b

,

A. Etenko

q

, M. Fallot

w

, F. von Feilitzsch

x

, J. Felde

i

, S.M. Fernandes

b

, V. Fischer

n

,

D. Franco

d

, M. Franke

x

, H. Furuta

z

, I. Gil-Botella

g

, L. Giot

w

, M. Göger-Neff

x

,

L.F.G. Gonzalez

af

, L. Goodenough

c

, M.C. Goodman

c

, C. Grant

i

, N. Haag

x

, T. Hara

p

,

J. Haser

s

, M. Hofmann

x

, G.A. Horton-Smith

o

, A. Hourlier

d

, M. Ishitsuka

ab

, J. Jochum

ad

,

C. Jollet

v

, F. Kaether

s

, L.N. Kalousis

ag

, Y. Kamyshkov

y

, D.M. Kaplan

l

, T. Kawasaki

t

,

E. Kemp

af

, H. de Kerret

d

,

ah

, T. Konno

ab

, D. Kryn

d

, M. Kuze

ab

, T. Lachenmaier

ad

,

C.E. Lane

j

, T. Lasserre

n

,

d

, A. Letourneau

n

, D. Lhuillier

n

, H.P. Lima Jr.

e

, M. Lindner

s

,

J.M. López-Castaño

g

, J.M. LoSecco

u

, B.K. Lubsandorzhiev

m

, S. Lucht

a

, J. Maeda

ac

,

C. Mariani

ag

, J. Maricic

j

, J. Martino

w

, T. Matsubara

ac

, G. Mention

n

, A. Meregaglia

v

,

T. Miletic

j

, R. Milincic

j

, A. Minotti

v

, Y. Nagasaka

k

, K. Nakajima

t

, Y. Nikitenko

m

,

P. Novella

d

, M. Obolensky

d

, L. Oberauer

x

, A. Onillon

w

, A. Osborn

y

, C. Palomares

g

,

I.M. Pepe

e

, S. Perasso

d

, P. Pfahler

x

, A. Porta

w

, G. Pronost

w

, J. Reichenbacher

b

,

B. Reinhold

s

, M. Röhling

ad

, R. Roncin

d

, S. Roth

a

, B. Rybolt

y

, Y. Sakamoto

aa

, R. Santorelli

g

,

F. Sato

ac

, A.C. Schilithz

e

, S. Schönert

x

, S. Schoppmann

a

, M.H. Shaevitz

h

, R. Sharankova

ab

,

S. Shimojima

ac

, V. Sibille

n

, V. Sinev

m

,

n

, M. Skorokhvatov

q

, E. Smith

j

, J. Spitz

r

, A. Stahl

a

,

I. Stancu

b

, L.F.F. Stokes

ad

, M. Strait

f

, A. Stüken

a

, F. Suekane

z

, S. Sukhotin

q

,

T. Sumiyoshi

ac

, Y. Sun

b

, R. Svoboda

i

, K. Terao

r

, A. Tonazzo

d

, H.H. Trinh Thi

x

,

G. Valdiviesso

e

, N. Vassilopoulos

v

, C. Veyssiere

n

, M. Vivier

n

, S. Wagner

s

, H. Watanabe

s

,

C. Wiebusch

a

, L. Winslow

r

, M. Wurm

ad

, G. Yang

c

,

l

, F. Yermia

w

, V. Zimmer

x

a_{III. Physikalisches Institut, RWTH Aachen University, 52056 Aachen, Germany}

b_{Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA} c_{Argonne National Laboratory, Argonne, IL 60439, USA}

d_{APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris Cité, 75205 Paris Cedex 13, France} e_{Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ, cep 22290-180, Brazil}

f_{The Enrico Fermi Institute, The University of Chicago, Chicago, IL 60637, USA}

g_{Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, CIEMAT, E-28040, Madrid, Spain} h_{Columbia University, New York, NY 10027, USA}

i_{University of California, Davis, CA 95616-8677, USA}

j_{Physics Department, Drexel University, Philadelphia, PA 19104, USA} k_{Hiroshima Institute of Technology, Hiroshima, 731-5193, Japan}

l_{Department of Physics, Illinois Institute of Technology, Chicago, IL 60616, USA} m_{Institute of Nuclear Research of the Russian Academy of Science, Russia}

n_{Commissariat à l’Energie Atomique et aux Energies Alternatives, Centre de Saclay, IRFU, 91191 Gif-sur-Yvette, France} o_{Department of Physics, Kansas State University, Manhattan, KS 66506, USA}

p_{Department of Physics, Kobe University, Kobe, 657-8501, Japan} q_{NRC Kurchatov Institute, 123182 Moscow, Russia}

r_{Massachusetts Institute of Technology, Cambridge, MA 02139, USA} s_{Max-Planck-Institut für Kernphysik, 69117 Heidelberg, Germany} t_{Department of Physics, Niigata University, Niigata, 950-2181, Japan}

http://dx.doi.org/10.1016/j.physletb.2014.04.045

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52 Double Chooz Collaboration / Physics Letters B 735 (2014) 51–56

u_{University of Notre Dame, Notre Dame, IN 46556-5670, USA}

v_{IPHC, Université de Strasbourg, CNRS/IN2P3, F-67037 Strasbourg, France}

w_{SUBATECH, CNRS/IN2P3, Université de Nantes, Ecole des Mines de Nantes, F-44307 Nantes, France} x_{Physik Department, Technische Universität München, 85747 Garching, Germany}

y_{Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA} z_{Research Center for Neutrino Science, Tohoku University, Sendai 980-8578, Japan} aa_{Tohoku Gakuin University, Sendai, 981-3193, Japan}

ab_{Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan} ac_{Department of Physics, Tokyo Metropolitan University, Tokyo, 192-0397, Japan}

ad_{Kepler Center for Astro and Particle Physics, Universität Tübingen, 72076 Tübingen, Germany} ae_{Universidade Federal do ABC, UFABC, Saõ Paulo, Santo André, SP, Brazil}

af_{Universidade Estadual de Campinas – UNICAMP, Campinas, SP, Brazil} ag_{Center for Neutrino Physics, Virginia Tech, Blacksburg, VA, USA}

ah_{Laboratoire Neutrino de Champagne Ardenne, domaine d’Aviette, 08600 Rancennes, France}

a r t i c l e

i n f o

a b s t r a c t

Article history:

Received 23 January 2014

Received in revised form 15 April 2014 Accepted 24 April 2014

Available online 9 May 2014 Editor: H. Weerts

The oscillation results published by the Double Chooz Collaboration in 2011 and 2012 rely on background models substantiated by reactor-on data. In this analysis, we present a background-model-independent measurement of the mixing angle θ13 by including 7.53 days of reactor-off data. A global ﬁt of the

observed antineutrino rates for different reactor power conditions is performed, yielding a measurement of bothθ13 and the total background rate. The results on the mixing angle are improved signiﬁcantly

by including the reactor-off data in the ﬁt, as it provides a direct measurement of the total background rate. This reactor rate modulation analysis considers antineutrino candidates with neutron captures on both Gd and H, whose combination yields sin2(2θ13)=0.102±0.028(stat.)±0.033(syst.). The results

presented in this study are fully consistent with the ones already published by Double Chooz, achieving a competitive precision. They provide, for the ﬁrst time, a determination ofθ13that does not depend on

a background model.

1. Introduction

Recently, three reactor neutrino experiments, Double Chooz[1], Daya Bay[2]and RENO[3]have successfully determined the lep-tonic mixing angle

θ

13to be clearly non-zero. These disappearance

experiments are sensitive to the oscillation amplitude and have measured sin2

(

2

θ

13

)

to be

∼

0

.

1. They identify reactor

antineutri-nos via the inverse beta decay (IBD) reaction

ν

¯

ep

→

e+n and use a

coincidence between the prompt positron and the delayed neutron capture signals in order to separate antineutrinos from background events. However, correlated events due to fast neutrons, stopping muons and cosmogenic generated radio-nuclides form a danger-ous background in experiments with shallow overburden. So far, all published results are based on background models, which are derived from data taken during reactor-on periods using certain as-sumptions about the origin of correlated background events. This procedure contributes, along with detection eﬃciency and reactor source errors, to the total systematic uncertainty. In this paper, we present a ﬁrst measurement of

θ

13which is free from background

assumptions.

Of the three experiments, Double Chooz is the only one to be exposed to only two reactors. The total antineutrino ﬂux therefore changes signiﬁcantly during reactor maintenance periods when one of the two reactor cores is not functioning. At certain times both cores at Chooz were turned off simultaneously, providing the unique opportunity to determine the background in a model inde-pendent way. In this paper we present an analysis of the Double Chooz data in which the background rate and the oscillation ampli-tude are determined simultaneously by analyzing the

ν

¯

ecandidate

rates for different reactor conditions ranging from zero to full ther-mal power. The background rate has been proven to be constant in time [4], thus being the same in all the considered reactor peri-ods. We restrict our analysis to rate measurements only. In order to identify antineutrino events via the inverse beta decay, we use

both neutron captures on Gd and on H. Finally, we present a com-bined Gd- and H-analysis and compare our ﬁnal result with the published ones that rely on the energy spectrum information. This analysis is also useful as a direct test of the background model used for the Double Chooz oscillation analysis. We will show that our background rate determination is in full agreement with the prediction derived from our background model.

2. Reactor Rate Modulation analysis

In order to measure the mixing angle

θ

13by means of reactor

neutrino experiments, the observed rate of

ν

¯

e candidates (Robs)

is compared with the expected one (Rexp_{). As Double Chooz data}

have been taken for different reactor thermal power ( Pth)

condi-tions, this comparison can be done for different expected averaged rates, in a Reactor Rate Modulation (RRM) analysis. In particular, there are three well-deﬁned reactor conﬁgurations: (1) the two reactors are on (2-On data), (2) one of the reactors is off (1-Off reactor data), and (3) both reactors are off (2-Off reactor data). For the 1-Off and 2-Off reactor data, the expected antineutrino rate takes into account the residual neutrinos (Rr-ν ) generated after the reactors are turned off as

β

decays keep taking place. While the antineutrino ﬂux generated during reactor operation is computed as described in[1], the rate of residual antineutrinos is estimated as described in[4].

From the comparison between Rexp and Robs at different reac-tor powers both the value of

θ

13 and the total background rate B

can be derived. The correlation of the expected and observed rates follows a linear model parametrized by sin2

(

2

θ

13

)

and B:

Robs

=

B

+

Rexp

=

B

+

1

−

sin2

(

2

θ

13

)

η

osc

Rν

,

(1)

where Rν is the expected rate of actual antineutrinos in absence of oscillation and

η

osc is the average disappearance coeﬃcient,

(4)

Fig. 1. Expected unoscillated antineutrino event rate as a function of the total

baseline-adjusted thermal power ( P∗th=

Nr

i P i

th/L 2

i), for the n-Gd and n-H

anal-yses. P∗_this presented in percentage of the nominal power.

sin2

(

m2L

/

4E

)

. This coeﬃcient is computed by means of sim-ulations for each one of the data points as the integration of the normalized antineutrino energy (E) spectrum multiplied by the os-cillation effect driven by

m2 (taken from [5]) and the distance

L between the reactor cores and the detector. The average

η

osc

value corresponding to the full data sample is computed to be 0.55. Fitting the data to the above model provides a direct mea-surement of the mixing angle and the total background rate. In previous Double Chooz publications [1,6], the rates and the en-ergy spectra of the three dominant background sources (fast neu-trons, stopping muons and cosmogenic isotope

β

-n decays) were estimated from reactor-on data, therefore building a background model that was ﬁtted along with the mixing angle. In contrast, the RRM analysis extracts the total background rate from data in a model-independent and inclusive way, where all background sources (even possible unknown ones) are accounted for. The ac-curacy and precision on the ﬁtted value of B, as well as on

θ

13,

rely mostly on the 2-Off reactor data, as this sample provides a powerful lever arm for the ﬁt. As the accidental background in the observed rate is known to 0.2% by means of the off-time coinci-dences, the RRM analysis is performed with accidental-subtracted candidate samples. Therefore, hereafter the total background B refers to all background sources except the accidental one. The RRM oscillation analysis can be performed separately with the

ν

¯

e

candidate samples obtained with neutron captures on Gd (n-Gd) and H (n-H), as well as with a combination of these.

In the current analysis, the data sample in[1,6] is used along with an extra 2-Off sample collected in 2012[4], which increases the total 2-Off run time to 7.53 days. Within the corresponding total live time of 233.93 days (246.4 days), 8257 (36 883) candi-dates (including accidental background) were found according to the n-Gd (n-H) selection, 8 (599) of which were observed during the 2-Off period. The number of antineutrino events expected to be observed in the reactor-on periods was 8440 (17 690). During the 1-Off period, the number of predicted residual events is 11.2 (28.7), while within the 2-Off period, 1.4 (3.7) residual events are expected in the n-Gd (n-H) selection. The data are distributed in 7 bins of Pth, corresponding to two different sets of bins of Rexp

for the n-Gd and n-H

ν

¯

ecandidate samples. The binning used for

this analysis is shown inFig. 1, where the expected rates are pre-sented as a function of the total baseline-adjusted thermal power,

P_th∗

=

Nr

i Pith

/

L2i, where Nr

=

2 is the number of reactors and Li

Fig. 2. Uncertainty in the n-Gdν¯eexpected rate for reactor-on data. Triangles show the rate error due to Pth uncertainty, while circles stand for the total rate error accounting for all reactor-related systematics sources, as described and estimated in[1].

is the distance between the detector and reactor i. The error bars in the expected rates (not visible for all data points) account for the systematic errors.

3. Systematic uncertainties

There are three sources of systematics to be accounted for in the RRM analysis: (1) detection eﬃciency (

σ

d), (2) residual

ν

¯

e

pre-diction in reactor-off data (

σ

ν ), and (3)

ν

¯

eprediction in reactor-on

data (

σ

r). The detection eﬃciency systematics in n-Gd (n-H)

ν

¯

e

sample are listed in [1] (see also [6]), from which the total un-certainty

σ

d is derived to be 1.01% (1.57%). The uncertainty in the

rate of residual antineutrinos has been computed with core evolu-tion simulaevolu-tions as described in[4]for the 1-Off and 2-Off reactor periods: a

σ

ν

=

30% error is assigned to Rr-ν . Finally, a dedicated

study has been performed in order to estimate

σ

ras a function of

the thermal power.

To a good approximation, all sources of reactor-related system-atics are independent of Pth, with the exception of the uncertainty

on Pth itself,

σ

P. This fractional error is 0.5% [1]when the

reac-tors are running at full power, but it increases as Pthdecreases. In

[1,6],

σ

P is assumed to be 0.5% for all data. This is a very good

ap-proximation when one integrates all the data taking samples, and consequently all reactor operation conditions, as more than 90% of the data are taken at full reactor power. However, this is not a valid approximation in the current analysis as it relies on sep-arating the data according to different reactor powers. In order to compute

σ

Pfor different Pth, an empirical model is ﬁtted to a

sam-ple of measurements provided by EdF (the company operating the Chooz nuclear plant). An effective absolute uncertainty of about 35 MW is derived from the ﬁt, being the dominant component of the model. This absolute error translates into a 1

/

Pth dependence

of the relative power uncertainty, which is used to compute the errors in Rexp. The resulting errors (both from Pth only and from

all reactor systematic sources listed in[1]) are shown inFig. 2, for the case of the n-Gd

ν

¯

e expectation. The total error

σ

ri (where i

stands for each data point) ranges from 1.75% (reactors operating at full power) to 1.92% (one or two reactors not at full power). In a conservative approach, the

σ

i

r errors are assumed to be fully

(5)

Fig. 3. RRM (sin2(2θ13),BGd) ﬁt with n-Gdν¯e candidates. Empty (solid) best-ﬁt point and C.L. regions show the results without (with) the 2-Off data sample.

4. Background independent oscillation results

The Robs _{ﬁt is based on a standard}

_χ

2 _{minimization. Without}

taking into account the 2-Off data, the

χ

2_{deﬁnition is divided into}

two different terms:

χ

2

₌

_χ

2

on

+

χ

pull2 , where

χ

2

on stands for 2-On

and 1-Off reactor data and

χ

2

pullaccounts for the systematic

uncer-tainties. Assuming Gaussian-distributed errors for the data points involving at least one reactor on,

χ

2

onis built as follows:

χ

2 on

=

N

i

(

Robs_i

−

Rexp_i

[

1

+

α

d

₊

_k i

α

r

+

wi

α

ν

] −

B

)

2

σ

2 stat

,

(2)

where N stands for the number of bins (6, as shown inFig. 1), and where

α

d_,

_α

r_and

_α

_{ν stand for pulls associated with the detection,}

reactor-on and residual antineutrino systematics, respectively. The weights ki are deﬁned as

σ

ri

/

σ

r, where

σ

r

=

1

.

75% stands for the

error when the cores operate at full power. The fraction of residual antineutrinos, wi, in each data point is deﬁned as wi

=

Rr-_iν

/

Rexp_i .

The term

χ

2

pullincorporates the penalty terms corresponding to

σ

r,

σ

dand

σ

ν :

χ

_pull2

=

α

d

σ

d

2

+

α

r

σ

r

2

+

α

ν

σ

ν

2

.

(3)

According to this

χ

2_{deﬁnition, a ﬁt to the two free parameters}

sin2

(

2

θ

13

)

and the total background rate BGd is performed with

the n-Gd candidates sample. The results are shown inFig. 3with best-ﬁt point (empty star) and C.L. intervals. The best ﬁt values are sin2

(

2

θ

13

)

=

0

.

21

±

0

.

12 and BGd

=

2

.

8

±

2

.

0 events

/

day, where the

errors correspond to

χ

2

₌

₂

_.

_{3. Although the precision is poor,}

these results are consistent within 1

σ

with the ones presented in[1]. In particular, the best ﬁt value for the background is consis-tent with the independent estimate in[1](1

.

9

±

0

.

6 events

/

day) and with the direct measurement obtained from the 2-Off data in[4]: B2Off

=

0

.

7

±

0

.

4 events

/

day (once accidental background is

subtracted).

In order to improve the RRM determination of sin2

(

2

θ

13

)

, the

2-Off data can be incorporated into the ﬁt as an additional data point for Pth

=

0 MW. The

χ

2 is built then as

χ

2

=

χ

on2

+

χ

off2

+

χ

2

pull. Due to the low n-Gd statistics in the 2-Off reactor period, the

Fig. 4. RRM ﬁt with n-Gd ν¯ecandidates including 2-Off data. The null oscillation hypothesis assuming the background estimates obtained in[1]is also shown for comparison purposes.

corresponding error in Robs_{is considered to be Poisson-distributed.}

As a consequence,

χ

2

off is deﬁned as a binned Poisson likelihood

following a

χ

2_{distribution:}

χ

_off2

=

2

Nobsln N obs B

+

Nexp

_[

₁

₊

_α

d

₊

_α

ν

_]

+

B

+

Nexp

1

+

α

d

+

α

ν

−

Nobs

,

(4)

where Nobs

₌

_Robs

_·

_T

off and Nexp

=

Rr-ν

·

Toff; Toff the live time of

the 2-Off data sample. The results of the (sin2

(

2

θ

13

),

B) ﬁt

includ-ing the 2-Off data are presented inFig. 3with solid best-ﬁt point and C.L. intervals. The best ﬁt values are sin2

(

2

θ

13

)

=

0

.

107

±

0

.

074

and BGd

=

0

.

9

±

0

.

6 events

/

day.

As the 2-Off data provide the most precise determination of the total background rate in a model-independent way, the in-troduction of this sample (or equivalently the value of B2Off) in

the RRM ﬁt provides a direct constraint to B. Therefore, hereafter we consider

θ

13 to be the only free parameter in the ﬁt, while

B is treated as a nuisance parameter. Therefore, the best ﬁt error

on

θ

13 corresponds to

χ

2

=

1. The outcome of the

correspond-ing ﬁt uscorrespond-ing the n-Gd sample can be seen in Fig. 4. The best ﬁt value of sin2

(

2

θ

13

)

is now 0

.

107

±

0

.

049, with a

χ

2

/

dof of

4.2/5. The value of

θ

13is in good agreement with the result of[1]

(sin2

(

2

θ

13

)

=

0

.

109

±

0

.

039), while the error is slightly larger due

to the fact that the RRM analysis does not incorporate energy spec-trum information. The RRM fit does not change the measurement of the total background rate provided by the 2-Off data signifi-cantly, as the best fit estimate of BGdis 0

.

9

±

0

.

4 events

/

day.

While the best ﬁt value of the total background rate depends on the antineutrino candidate selection cuts, the best ﬁt of

θ

13

must be independent of these cuts. In order to cross-check the above results, the RRM analysis has also been performed for a different set of selection cuts: those applied in the ﬁrst Double Chooz oscillation analysis[7]. This selection does not make use of the muon outer veto (OV) and does not apply a showering muon veto. Therefore, the number of correlated background events in the

¯

ν

e candidates sample is increased (according to the estimates, by

1.3 events/day). In this case, the input value for the background rate provided by the 2-Off data is B2Off

=

2

.

4

±

0

.

6 events

/

day[4].

(6)

with the above results, while the background rate is not signiﬁ-cantly modiﬁed either in this case (BGd

=

2

.

6

±

0

.

6 events

/

day).

As shown in[6], the precision of the oscillation analysis based on n-H captures is not as good as the n-Gd one due to the larger systematic uncertainties and the larger accidental contam-ination. This applies also to the RRM analysis. The n-H ﬁt yields sin2

(

2

θ

13

)

=

0

.

091

±

0

.

078 (B2Off

=

10

.

8

±

3

.

4 events

/

day, BH

=

8

.

7

±

2

.

5 events

/

day) with

χ

2

_/

_dof

₌

₄

_.

₈

_/

_{5, consistent with the}

re-sults in [6](sin2

(

2

θ

13

)

=

0

.

097

±

0

.

048). The n-H candidates can

be ﬁtted together with the n-Gd ones in order to increase the pre-cision of the analysis and to test the consistency of both selections. In order to perform a global ﬁt, a combined

χ

2 _{is built from the}

sum of the Gd and H ones:

χ

2

=

χ

_Gd2

+

χ

_H2

+

χ

_pull2

.

(5)

While

σ

r and

σ

ν are fully correlated between the n-Gd and

n-H candidates samples (they do not depend on selection cuts, but on reactor parameters), there is a partial correlation (

ρ

) in the detection eﬃciency uncertainty, which has been estimated to be at the level of 9%. This overall factor comes from correlated and anti-correlated contributions. The correlated contributions are due to the spill-in/out events (IBD events in which the prompt and the delayed signal do not occur in the same detection volume, as deﬁned in[1]) and the number of protons in the detection vol-umes. The anti-correlated contribution is due to the uncertainty in the fraction of neutron captures in Gd and H. From this

ρ

value, one can decompose

σ

dinto uncorrelated (

σ

_Gd-ud

=

0

.

91% and

σ

d

H-u

=

1

.

43%) and correlated contributions (

σ

cd

=

0

.

38%) for the

n-Gd and n-H data. The pull

α

d_{in Eq.}₍₃₎_{is now divided into three}

terms accounting for the correlated and uncorrelated parts of the detection error:

α

d

Gd-u,

α

H-ud and

α

cd. Accordingly,

χ

pull2 is deﬁned

as:

χ

_pull2

=

α

d Gd-u

σ

d Gd-u

2

+

α

d H-u

σ

d H-u

2

+

α

d c

σ

d c

2

+

α

r

σ

r

2

+

α

ν

σ

ν

2

.

(6)

The combined Gd-H RRM ﬁt is shown in Fig. 5. The best ﬁt value of the mixing angle is sin2

(

2

θ

13

)

=

0

.

102

±

0

.

028

(

stat.

)

±

0

.

033

(

syst.

)

, for

χ

2

_/

_dof

₌

₈

_.

₀

_/

_{11. This value is consistent within}

1

σ

with respect to the single n-Gd and n-H results, while the pre-cision is slightly improved. The relative error on sin2

(

2

θ

13

)

goes

from 46% to 42%. As in the previous results, the output values of the total background rates are consistent with the input values:

BGd

=

0

.

9

±

0

.

4 events

/

day and BH

=

9

.

0

±

1

.

5 events

/

day. The

im-pact of the correlated part in

σ

d _{has been proven to be negligible}

by performing a ﬁt assuming no correlation. 5. Comparison of Double Chooz

θ

13results

Including this novel RRM analysis, Double Chooz has released four different

θ

13 analysis results. These results are obtained as

follows: (1) with n-Gd candidates in[1], (2) with n-H candidates in[6], (3) with n-Gd candidates and the RRM analysis, and (4) with n-H candidates and the RRM analysis. Beyond the common detec-tion and reactor-related systematics, these four analyses rely on two different candidate samples (n-H and n-Gd), and two different analysis techniques (rate

+

shape ﬁt with background inputs and RRM). The four sin2

(θ

13

)

values obtained are presented inFig. 6,

as well as the combined Gd-H RRM result. All the values are con-sistent within 1

σ

with respect to the most precise result, which is provided by the rate

+

shape ﬁt.

Fig. 5. RRM combined ﬁt using n-Gd and n-Hν¯ecandidates.

Fig. 6. Summary of published Double Chooz results onθ13: the n-Gd[1]and n-H

[6]rate plus shape (RS) results, and the n-Gd and n-H RRM ones. For comparison purposes, the combined Gd-H RRM result is also shown. The shaded region shows the 68% C.L. interval of the n-Gd RS ﬁt.

6. Summary and conclusions

While the oscillation results published by the Double Chooz Collaboration in [1,6,7]rely on a background model derived from reactor-on data, the RRM analysis is a background model indepen-dent approach. Both

θ

13 and the total background rate are

de-rived without model assumptions on the background by a global ﬁt to the observed antineutrino rate as a function of the non-oscillated expected rate for different reactor power conditions. Al-though the RRM ﬁt with only reactor-on data does not achieve a competitive precision on

θ

13, it provides an independent

de-termination of the total background rate. This rate is consistent with the Double Chooz background model and with the measure-ment of the total background from the 7.53 days of reactor-off data[4]. As this 2-Off sample provides the most precise determi-nation of the total background rate in a model independent way, it is introduced in the RRM analysis in order to improve the re-sults on

θ

13, which remains as the only free parameter in the ﬁt.

The best ﬁt value of sin2

(

2

θ

13

)

=

0

.

107

±

0

.

049 is found by

(7)

further improved by combining the n-Gd and n-H

ν

¯

e samples:

sin2

(

2

θ

13

)

=

0

.

102

±

0

.

028

(

stat.

)

±

0

.

033

(

syst.

)

. The outcome of the

RRM ﬁt is consistent within 1

σ

with the already published results for

θ

13, yielding a competitive precision. Beyond the cross-check of

the background estimates in the Double Chooz oscillation analyses, the RRM analysis provides, for the ﬁrst time, a background model independent determination of the

θ

13mixing angle.

Acknowledgements

We thank the French electricity company EDF; the European fund FEDER; the Région de Champagne Ardenne; the Départe-ment des Ardennes; and the Communauté des Communes Ar-dennes Rives de Meuse. We acknowledge the support of the CEA, CNRS/IN2P3, the computer center CCIN2P3, and LabEx UnivEarthS in France; the Ministry of Education, Culture, Sports, Science, and Technology of Japan (MEXT) and the Japan Society for the Promo-tion of Science (JSPS); the Department of Energy and the NaPromo-tional Science Foundation of the United States; the Ministerio de Cien-cia e Innovación (MICINN) of Spain; the Max Planck Gesellschaft, and the Deutsche Forschungsgemeinschaft DFG (SBH WI 2152), the Transregional Collaborative Research Center TR27, the excellence

cluster “Origin and Structure of the Universe”, and the Maier-Leibnitz-Laboratorium Garching in Germany; the Russian Academy of Sciences, the Kurchatov Institute and RFBR (the Russian Founda-tion for Basic Research); the Brazilian Ministry of Science, Technol-ogy and Innovation (MCTI), the Financiadora de Estudos e Projetos (FINEP), the Conselho Nacional de Desenvolvimento Cientíﬁco e Tecnológico (CNPq), the São Paulo Research Foundation (FAPESP), and the Brazilian Network for High Energy Physics (RENAFAE) in Brazil.

References

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